Hi guys,
Please help me with the following:
1) If (x  2y)(x + 2y) = 5 and (2x  y)(2x + y) = 35, then x^2y^2 / x^2+y^2
(A) 8/5
(B) 4/5
(C) 0
(D) 4/5
(E) 7/5
2)If l/m+n=m/n+1=n/l+m=k,where k is a real number, then which one of the following does k equal?
(A) 1/3
(B) 1/2
(C) 1
(D) 2
(E) 3
Please help.
Thank you.
Source  GMAT Math Bible  Nova  Equations
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For question 1), you can solve as following :
After expanding the two equation given in the problem, you get the following :
x^2  4y^2 = 5 .....(i)
4x^2  y^2 = 35.....(ii)
Add the two equations and you get following :
5x^2  5y^2 = 40
Therefore, x^2  y^2 = 8.... (a)
Now subtract (i) from (ii)
3x^2 + 3y^2 = 30
Therefore, x^2 + y^2 = 10.....(b)
Divide (a) by (b) and you get = 8/10 = 4/5
Answer is [spoiler](d)[/spoiler]
After expanding the two equation given in the problem, you get the following :
x^2  4y^2 = 5 .....(i)
4x^2  y^2 = 35.....(ii)
Add the two equations and you get following :
5x^2  5y^2 = 40
Therefore, x^2  y^2 = 8.... (a)
Now subtract (i) from (ii)
3x^2 + 3y^2 = 30
Therefore, x^2 + y^2 = 10.....(b)
Divide (a) by (b) and you get = 8/10 = 4/5
Answer is [spoiler](d)[/spoiler]

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For question 2)
L/m+n = k
therefore, L/k = m+n
Similarly, m/k = n+L
n/k = L+m
Add all three equations :
1/k (m+n+L) = 2(m+n+L)
Therefore k = 1/2
Answer = B
L/m+n = k
therefore, L/k = m+n
Similarly, m/k = n+L
n/k = L+m
Add all three equations :
1/k (m+n+L) = 2(m+n+L)
Therefore k = 1/2
Answer = B
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(x  2y)(x + 2y) = 5 and (2x  y)(2x + y) = 35, then (xÂ²  yÂ²) / (xÂ² + yÂ²)shanice wrote:Hi guys,
Please help me with the following:
1) If (x  2y)(x + 2y) = 5 and (2x  y)(2x + y) = 35, then x^2y^2 / x^2+y^2
(A) 8/5
(B) 4/5
(C) 0
(D) 4/5
(E) 7/5
Please help.
Thank you.
(x  2y)(x + 2y) = 5 implies xÂ²  4yÂ² = 5 ... Equation (1)
(2x  y)(2x + y) = 35 implies 4xÂ²  yÂ² = 35 ... Equation (2)
Adding equations (1) and (2), 5xÂ²  5y = 40 or xÂ²  yÂ² = 8
Subtracting equation (1) from equation (2), 3xÂ² + 3yÂ² = 30 or xÂ² + yÂ² = 10
Therefore, (xÂ²  yÂ²) / (xÂ² + yÂ²) = 8/10 or [spoiler]4/5[/spoiler]
The correct answer is D.
Anurag Mairal, Ph.D., MBA
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shanice wrote: 2)If l/m+n=m/n+1=n/l+m=k,where k is a real number, then which one of the following does k equal?
(A) 1/3
(B) 1/2
(C) 1
(D) 2
(E) 3
quote]
l
 = k
(m+n)
=> l = k(m+n)
Similarly
m = k(n+l)
n = k(l+m)
Now add all the above three equations
l+m+n = k(m+n) + k(n+l) + k(l+m)
l+m+n = 2k(l+m+n)
1 = 2k
k = 1/2
Answer = B